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Name: __________________________ Date: _____________ 1. An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. The null and alternate hypotheses you would use to test this claim are 2. Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. Net weights actually vary slightly from bag to bag and are Normally distributed with a mean . A representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised and so intends to test the hypotheses H o : 14; H a : 14 To do this, he selects 16 bags of this brand at random and determines the net weight of each. He finds that the sample mean to be x 13.82 and the sample standard deviation to be s 0.24 . We conclude that we would 3. A type I error in the previous question would mean 4. You are thinking of using a t procedure to test hypotheses about the mean of a population using a significance level of 0.05. You suspect that the distribution of the population is not Normal and may be moderately skewed. Which of the following statements is correct? 5. After once again losing a football game to the archrival, a college’s alumni association conducted a survey to see if alumni were in favor of firing the coach. An SRS of 100 alumni from the population of all living alumni was taken. 64 of the alumni in the sample were in favor of firing the coach. Suppose you wish to see if a majority of living alumni are in favor of firing the coach. The appropriate test statistic is 6. We prefer the t procedures to the z procedures for inference about a population mean because 7. Looking online (for example, at espn.go.com) you find the salaries of all 22 players for the Chicago Cubs as of opening day of the 2005 baseball season. The club total was $87 million, eighth in the major leagues. Which inference procedure would you use to estimate the average salary of the Cubs players? 8. You read in the report of a psychology experiment that “separate analyses for our two groups of 12 participants revealed no overall placebo effect for our student group (mean =0.08, SD = 0.37, t(11) = 0.49) and a significant effect for our non-student group (mean = 0.35, SD = 0.37, t(11) = 0.38, p < 0.01).” Are the two values given for the t test statistic correct? (The null hypothesis is that the mean effect is zero.) 9. A sociologist is studying the effect of having children within the first two years of marriage on the divorce rate. Using hospital birth records, she selects a random sample of 200 couples who had a child within the first two years of marriage. Following up on these couples, she finds that 80 couples are divorced within 5 years. To determine if having children within the first two years of marriage increases the divorce rate we should test 10. In order to study the amounts owed to a particular city, a city clerk takes a random sample of 16 files from a cabinet containing a larger number of delinquent accounts and finds the average amount x owed to the city to be $230 with a sample standard deviation of $36. It has been claimed that the true mean amount owed on accounts of this type is greater than $250. If it is appropriate to assume that the amount owed is a Normally distributed random variable, the value of the test statistic appropriate for testing the claim is 11. What is the value of t * , the critical value of the t distribution with 8 degrees of freedom, which satisfies the condition that the probability is 0.10 of being larger than t * ? 12. Which of the following 95% confidence intervals would lead us to reject H o : p 0.30 in favor of H a : p 0.30 at the 5% significance level? An SRS of 100 postal employees found that the average time these employees had worked at the postal service was x =7 years with a standard deviation of s = 2 years. Are these data evidence that the mean for the population of postal employees has changed from the value of 7.5 years 20 years ago? To determine this, we test the hypotheses H o : 7.5; H a : 7.5 with a one-sample t test. 13. What conclusion should you draw from a test at the 5% significance level? 14. Suppose we are not sure if the population distribution is Normal. In which of the following circumstances would use of the t procedure yield misleading results? 15. You have data on rainwater collected at 6 locations in the Adirondack Mountains of New York State. One measurement is the acidity of the water, measured by pH on a scale of 0 to 14 (the pH of distilled water is 7.0). Which inference procedure would you use to estimate the average acidity of rainwater in the Adirondacks?
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